Question

Estimate the theoretical fracture strength of a brittle material if it is known that fracture occurs by the propagation of an elliptically shaped surface crack of length 0.28 mm and that has a tip radius of curvature of 0.002 mm when a stress of 1430 MPa is applied.

Answer 1

theoretical fracture strength = 16919.98 MPa

Step-by-step explanation:

given data

Length (L) = 0.28 mm = 0.28 × 10⁻³ m

radius of curvature (r) = 0.002 mm = 0.002 × 10⁻³ m

Stress (s₀) = 1430 MPa = 1430 × 10⁶ Pa

solution

we get here theoretical fracture strength s that is express as

theoretical fracture strength =
`s_(0) * \sqrt{(L)/(r) }` .............................1

put here value and we get

theoretical fracture strength =
`1430 * 10^6* \sqrt{(0.28* 10^(-3))/(0.002* 10^(-3)) }`

theoretical fracture strength =
`16919.98 * 10^6`

theoretical fracture strength = 16919.98 MPa